The incident happened Thursday around 9:30 p.m. in the 1800 block of W. Mount Houston.
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Authorities say the father got into some sort of argument with the suspect. That suspect pulled out a gun, and the father tried to drive off.
The gunman shot at the car, which set off fireworks in the vehicle, causing it to catch fire, deputies say.
"Family had bought fireworks. It is believed gunfire struck the fireworks causing them to ignite," Harris County Sheriff Ed Gonzalez said.
Dramatic video shows flames overtaking the car.
The two children, a 1-year-old and 2-years-old, suffered extensive burns and are in critical condition.
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Investigators said some good Samaritans came to the rescue to help the family to an ER clinic.
"As far the suspect vehicle, we know it was a male who was in a newer model, light-colored Ford Expedition," said Deputy Tom Turner with HCSO Violent Crimes.
Turner said the suspect took off in the vehicle with possibly a woman and two other people.